Related papers: Finite elements for symmetric tensors in three dim…
We present a simple finite element method for the discretization of Reissner--Mindlin plate equations. The finite element method is based on using the nonconforming Crouzeix-Raviart finite element space for the transverse displacement, and…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of $C^0$ vertex continuity of stresses introduced recently by…
We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equations posed on evolving surfaces and bulk domains as well…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
In this work we introduce novel stress-only formulations of linear elasticity with special attention to their approximate solution using weighted residual methods. We present four sets of boundary value problems for a pure stress…
We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. These finite element spaces are essential for achieving…
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…
We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…
Explicit relations of matrices for two-dimensional finite element method with third-order triangular elements are given. They are more simple than relations presented in other works and could be easily implemented in new algorithms for both…
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of the harmonic energy of two two-dimensional vector fields,…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
This paper constructs a unified family of nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$ ($0\leqslant k\leqslant n$, $n\geqslant 1$). The spaces employ piecewise Whitney forms as shape functions, and include the…
This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to…
We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…
We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine…
We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector,…